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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlinePeter and Francesca just had business cards made. Peter's printing company charged a one-time setup fee of $14\$14 and then $8\$8 per box of cards. Francesca, meanwhile, ordered hers online. They cost $6\$6 per box. There was no setup fee, but she had to pay $16\$16 to have her order shipped to her house. By coincidence, Peter and Francesca ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy?\newlinePeter and Francesca each spent $\$_____ on business cards, buying _____ boxes.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlinePeter and Francesca just had business cards made. Peter's printing company charged a one-time setup fee of $14\$14 and then $8\$8 per box of cards. Francesca, meanwhile, ordered hers online. They cost $6\$6 per box. There was no setup fee, but she had to pay $16\$16 to have her order shipped to her house. By coincidence, Peter and Francesca ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy?\newlinePeter and Francesca each spent $\$_____ on business cards, buying _____ boxes.
  1. Set up equations: Let's set up the equations for Peter and Francesca's spending on business cards. Peter's total cost includes a setup fee and a per-box charge, while Francesca's includes a per-box charge and a shipping fee.
  2. Isolate variable: Solve for one variable using substitution. Let's isolate x x in Peter's equation.
  3. Substitute back: Substitute x x back into one of the original equations to find y y . We'll use Francesca's equation for simplicity.

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